Question 3
How many 25-tuples $(x_1, x_2, \dots, x_{25})$ of non-negative integers are there which satisfy the following identity?
$$
x_1^2 + x_2^2 + \dots + x_{25}^2 = 2 + x_1x_2 + x_2x_3 + \dots + x_{24}x_{25}.
$$
$$
x_1^2 + x_2^2 + \dots + x_{25}^2 = 2 + x_1x_2 + x_2x_3 + \dots + x_{24}x_{25}.
$$